I mean, a Supermutant is something you're not supposed to really want to be in Fallout 1 (it's something they threaten you with, at one point.) Or ghoul, even.
Actually, Fallout 1 was originally meant to continue as a super mutant even if you're dipped by the Master, but they had to cut it because of time constraints.
The various heroes have been the Vault Dweller, Chosen One (Tribal), and Brotherhood of Steel Initiate if you count Tactics. But when Bethesda got the rights, of course they wanted to recreate the experience of the original games for new fans, so you start out as a Vault Dweller again.
The official nicknames for the PCs are Vault Dweller (FO1), Chosen One (FO2), Lone Wanderer (FO3), The Warrior (Tactics) the Prisoner (Van Buren).
I think I like the formula wherein the player is a vault-dweller who has to leave his/her vault and venture outside. And it wouldn't make sense for you to be a vault-dweller if you were not a human.
You were a vault dweller only in Fallout 1 and 3. In Fallout 2 you were a tribal, and in Van Buren you were not going to be a vault dweller either. In Fallout 3, they made you a vault dweller again, in order to reintroduce vaults to the new audience, but they can make you start as something else in future sequels.
What is a feral Ghoul? It's a Ghoul who got radiated even more and lost his mind. Sounds reasonable to me.
It's not their existence that doesn't fit, it's their prevalence. There are far too many of them compared to normal ghouls.
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Asking for races is like asking for classes. It's not gonna happen. It's just not Fallouty!
I don't really mind playable super mutants and ghouls, but it would require changing the plot and dialogues substantially for each of them, not just changing your stats like Oblivion races do.